Why do unstable nuclei emit alpha, beta and gamma particles?

[Aspiring Girl]

Radioactive things radiate alpha, beta and gamma particles to achieve stability. As nucleus also emits these particles, can we say nucleus is unstable?

 

[e.bar.goum]

Radioactive things radiate alpha, beta and gamma particles to achieve stability. As nucleus also emits these particles, can we say nucleus is unstable?

The "radioactive things" that emit alpha beta and gamma particles are nuclei. So, yes. (but not all nuclei are unstable/radioactive!)

Let me re-write your statement:

"Radioactive nuclei emit alpha, beta and gamma particles to achieve stability. Such nuclei are unstable"